(b) Consider the experiment of picking a random point in the rectangle where the

Question

(b) Consider the experiment of picking a random point in the rectangle where the probability of the point being in any particular region contained within R is the area of that region. Let A1 and B1 be rectangles contained within R, with areas not equal to 0 or 1. Let A be the event that the random point is in A1, and B be the event that the random point is in B1. Give a geometric description of when it is true that A and B are independent. Also, give an example where they are independent and another example where they are not independent.

Explanation / Answer

for independence P(A n B) = P(A)*P(B) i.e Area(A1)*Area(B1) = Area (intersetion region )

so A and B are independent when regions are common area and satifying the condition  Area(A1)*Area(B1) = Area (intersetion region )

Area(A1) = 0.1,Area(B1) = 0.1 Area(common region) = 0.01 independent

Area(A1) = 0.1,Area(B1) = 0.1 Area(common region) = 0.05 dependent

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